6. The total population of a village is 5000. The number of males and females increases by 10% and 15% respectively and consequently the population of the village becomes 5600. what was the number of males in the village ?

As Theft is discovered at 3:00pm but Thief stole the car at 2:30.
This means thief covered some distance in this 30 min gap.
Distance travelled by thief in 30 min = 60 * 1/2 = 30 km

Owner Discovered Car at 3:00pm

Now relative speed = (75-60)km/hr = 15km/hr
Time needed to travel 30km by the speed of 15km/hr.
Time at which owner meets thief = 30/15 = 2 hrs
So After 2 hrs (i.e,at 5:00 pm) the owner will catch/overtake the thief

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8. Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg

Time taken by tap A to fill the cistern=4 hrs
so work done by tap A in 1 hour = 1/4th
Time taken by tap B to empty the full cistern = 9 hours
so work done by tap B in 1 hour = 1/9th
=> Work done by (A + B) in 1 hour=(1/4 - 1/9)=5/36
Therefore, the tank will fill the cistern = 36/5 hours=7.2 hours.

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10. Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages ?